In-plane formulation (Electrical Machine)

By

The inverse problem, to calculate a current density distribution for an imposed magnetic field can be obtained by using an in-plane formulation. Applying the Maxwell equation (3.8) and using the magnetic scalar and electric vector potential yields a particulartmp10278_thumb

tmp10280_thumb

Finally the in-planetmp10281_thumbvalid in the time domain, is described by:

tmp10284_thumb

In the frequency domain, by assuming a sinusoidal magnetic field and substitutingtmp10285_thumbit can be written:

tmp10288_thumb

This formulation is very similar to the A-formulation of the magnetic field and can be solved with the same methods. This formulation can not be applied to non-conducting regions. There,

tmp10289_thumb

must be evaluated.

In-planeformulation.

Fig. 4.5. In-planetmp10291_thumbformulation.